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Block #2,212,969

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2017, 4:54:33 AM Β· Difficulty 10.9439 Β· 4,614,107 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2493bc4d77e32c50d39fa507ae084349290aff593f6579039239ffc89dc46fe4
View on Chainz β†—

Height

#2,212,969

Difficulty

10.943893

Transactions

2

Size

427 B

Version

2

Bits

0af1a2f8

Nonce

69,087,916

Timestamp

7/19/2017, 4:54:33 AM

Confirmations

4,614,107

Mined by

⛏️ P2SHAU5Txf5eV2t6MozXJtFuZ3FkB3LVd6wNAg

Merkle Root

c82961ee191a17d542d28254c45d59d0af39016435b0becfbe86f13718dd4830
Transactions (2)
Coinbaseb747779dc1a4b6…d2386413d51e85
1 in β†’ 1 out8.3500 XPM110 B
AU5Txf5e…LVd6wNAg
1d68a8eebf418c…43cd5b310b463f
1 in β†’ 2 out13887.6262 XPM226 B
AJySnNqu…3adXwvucAKPtzMLg…UVa5UwHH
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.

2.422 Γ— 10⁹⁷(98-digit number)
24228356626405387330…49522394955774402559
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
2.422 Γ— 10⁹⁷(98-digit number)
24228356626405387330…49522394955774402559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.422 Γ— 10⁹⁷(98-digit number)
24228356626405387330…49522394955774402561
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
4.845 Γ— 10⁹⁷(98-digit number)
48456713252810774661…99044789911548805119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.845 Γ— 10⁹⁷(98-digit number)
48456713252810774661…99044789911548805121
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
9.691 Γ— 10⁹⁷(98-digit number)
96913426505621549323…98089579823097610239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.691 Γ— 10⁹⁷(98-digit number)
96913426505621549323…98089579823097610241
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
1.938 Γ— 10⁹⁸(99-digit number)
19382685301124309864…96179159646195220479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.938 Γ— 10⁹⁸(99-digit number)
19382685301124309864…96179159646195220481
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
3.876 Γ— 10⁹⁸(99-digit number)
38765370602248619729…92358319292390440959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.876 Γ— 10⁹⁸(99-digit number)
38765370602248619729…92358319292390440961
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
7.753 Γ— 10⁹⁸(99-digit number)
77530741204497239458…84716638584780881919
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:57,860,792 XPMΒ·at block #6,827,075 Β· updates every 60s
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