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Block #2,244,098

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2017, 4:22:17 PM Β· Difficulty 10.9470 Β· 4,597,230 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
40409b3af29be6357b71db87c7362cf215af14f350493b4c32247b3985437c55
View on Chainz β†—

Height

#2,244,098

Difficulty

10.947020

Transactions

1

Size

200 B

Version

2

Bits

0af26fe9

Nonce

1,065,155,913

Timestamp

8/9/2017, 4:22:17 PM

Confirmations

4,597,230

Mined by

⛏️ P2SHALJdD2vJVXDVh8ynZmYj5vFHpnvVGj5cds

Merkle Root

69c05a86beb76899afdb1f10c2610bfb506eb2ea0357c83e2e3c8ea57eb8b984
Transactions (1)
Coinbase69c05a86beb768…3c8ea57eb8b984
1 in β†’ 1 out8.3300 XPM110 B
ALJdD2vJ…vVGj5cds
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.

4.527 Γ— 10⁹⁴(95-digit number)
45277617439676938349…75763008322257332959
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
4.527 Γ— 10⁹⁴(95-digit number)
45277617439676938349…75763008322257332959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.527 Γ— 10⁹⁴(95-digit number)
45277617439676938349…75763008322257332961
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
9.055 Γ— 10⁹⁴(95-digit number)
90555234879353876699…51526016644514665919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.055 Γ— 10⁹⁴(95-digit number)
90555234879353876699…51526016644514665921
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
1.811 Γ— 10⁹⁡(96-digit number)
18111046975870775339…03052033289029331839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.811 Γ— 10⁹⁡(96-digit number)
18111046975870775339…03052033289029331841
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
3.622 Γ— 10⁹⁡(96-digit number)
36222093951741550679…06104066578058663679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.622 Γ— 10⁹⁡(96-digit number)
36222093951741550679…06104066578058663681
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
7.244 Γ— 10⁹⁡(96-digit number)
72444187903483101359…12208133156117327359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.244 Γ— 10⁹⁡(96-digit number)
72444187903483101359…12208133156117327361
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
1.448 Γ— 10⁹⁢(97-digit number)
14488837580696620271…24416266312234654719
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:57,974,987 XPMΒ·at block #6,841,327 Β· updates every 60s
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