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Block #837,848

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 12/3/2014, 5:00:50 AM Β· Difficulty 10.9753 Β· 5,988,725 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
3aedcf66673a49750093a5b93b831fd76d3cab6579781f13143177b97524a650
View on Chainz β†—

Height

#837,848

Difficulty

10.975309

Transactions

1

Size

243 B

Version

2

Bits

0af9ade0

Nonce

1,180,155,335

Timestamp

12/3/2014, 5:00:50 AM

Confirmations

5,988,725

Mined by

⛏️ P2SHAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

03f967407aa2f90bf17d7f91a56857fadb6bc68a21d60b586b0bd41184068775
Transactions (1)
Coinbase03f967407aa2f9…0bd41184068775
1 in β†’ 2 out8.2900 XPM152 B
AYFivgcJ…FT8wELGFALPu3s2c…EJXLjVFh
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.487 Γ— 10⁹⁷(98-digit number)
14877364290941584273…12382609207094644479
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.487 Γ— 10⁹⁷(98-digit number)
14877364290941584273…12382609207094644479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.487 Γ— 10⁹⁷(98-digit number)
14877364290941584273…12382609207094644481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.975 Γ— 10⁹⁷(98-digit number)
29754728581883168546…24765218414189288959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.975 Γ— 10⁹⁷(98-digit number)
29754728581883168546…24765218414189288961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.950 Γ— 10⁹⁷(98-digit number)
59509457163766337092…49530436828378577919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.950 Γ— 10⁹⁷(98-digit number)
59509457163766337092…49530436828378577921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.190 Γ— 10⁹⁸(99-digit number)
11901891432753267418…99060873656757155839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.190 Γ— 10⁹⁸(99-digit number)
11901891432753267418…99060873656757155841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.380 Γ— 10⁹⁸(99-digit number)
23803782865506534836…98121747313514311679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.380 Γ— 10⁹⁸(99-digit number)
23803782865506534836…98121747313514311681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.760 Γ— 10⁹⁸(99-digit number)
47607565731013069673…96243494627028623359
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
4.760 Γ— 10⁹⁸(99-digit number)
47607565731013069673…96243494627028623361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,856,733 XPMΒ·at block #6,826,572 Β· updates every 60s
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