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Block #2,468,441

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2018, 7:39:00 PM Β· Difficulty 10.9602 Β· 4,373,064 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c26bb56014dc18d9856b77a85869467bc880b5e2303ec27fe0e8bf79dbbe6174
View on Chainz β†—

Height

#2,468,441

Difficulty

10.960237

Transactions

2

Size

1015 B

Version

2

Bits

0af5d217

Nonce

354,950,522

Timestamp

1/11/2018, 7:39:00 PM

Confirmations

4,373,064

Mined by

⛏️ P2SHATcwxPA2az76gFEu7Yw8sV1TYTF2ugZWy7

Merkle Root

ef4cee4e59d487a41b5aace15b4783c5d4049271b7933531f54288117ac70104
Transactions (2)
Coinbase7c99ca09adcf07…371442c9e9bfc6
1 in β†’ 1 out8.3200 XPM109 B
ATcwxPA2…F2ugZWy7
8764b4e1d82f5e…0ad58612640e3f
5 in β†’ 2 out1546.2527 XPM816 B
AWVBExAa…uTCRpYY4ARugRuv1…DnSfzd3c
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.

4.077 Γ— 10⁹⁡(96-digit number)
40776399656417775195…13875942718698044479
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
4.077 Γ— 10⁹⁡(96-digit number)
40776399656417775195…13875942718698044479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.077 Γ— 10⁹⁡(96-digit number)
40776399656417775195…13875942718698044481
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
8.155 Γ— 10⁹⁡(96-digit number)
81552799312835550390…27751885437396088959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.155 Γ— 10⁹⁡(96-digit number)
81552799312835550390…27751885437396088961
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
1.631 Γ— 10⁹⁢(97-digit number)
16310559862567110078…55503770874792177919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.631 Γ— 10⁹⁢(97-digit number)
16310559862567110078…55503770874792177921
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
3.262 Γ— 10⁹⁢(97-digit number)
32621119725134220156…11007541749584355839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.262 Γ— 10⁹⁢(97-digit number)
32621119725134220156…11007541749584355841
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
6.524 Γ— 10⁹⁢(97-digit number)
65242239450268440312…22015083499168711679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.524 Γ— 10⁹⁢(97-digit number)
65242239450268440312…22015083499168711681
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
1.304 Γ— 10⁹⁷(98-digit number)
13048447890053688062…44030166998337423359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,976,419 XPMΒ·at block #6,841,504 Β· updates every 60s
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