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Block #2,268,824

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/26/2017, 12:13:46 PM Β· Difficulty 10.9527 Β· 4,562,415 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa31ed436f0355e6cd73d4dc1fca1b760f0ce64c74a345eeabba9133bba5061a
View on Chainz β†—

Height

#2,268,824

Difficulty

10.952681

Transactions

1

Size

200 B

Version

2

Bits

0af3e2ea

Nonce

179,913,036

Timestamp

8/26/2017, 12:13:46 PM

Confirmations

4,562,415

Mined by

⛏️ P2SHAeu7vVuCfQYff6tYGHiZsbmzyr3maUwjFU

Merkle Root

c798fe7d0de78be2a2b8f072df98f36d3d85457a673da9a4cdcb748dd95bb0c6
Transactions (1)
Coinbasec798fe7d0de78b…cb748dd95bb0c6
1 in β†’ 1 out8.3200 XPM110 B
Aeu7vVuC…3maUwjFU
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.

8.909 Γ— 10⁹⁴(95-digit number)
89093453685818171190…99882896267632201759
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
8.909 Γ— 10⁹⁴(95-digit number)
89093453685818171190…99882896267632201759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.909 Γ— 10⁹⁴(95-digit number)
89093453685818171190…99882896267632201761
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
1.781 Γ— 10⁹⁡(96-digit number)
17818690737163634238…99765792535264403519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.781 Γ— 10⁹⁡(96-digit number)
17818690737163634238…99765792535264403521
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
3.563 Γ— 10⁹⁡(96-digit number)
35637381474327268476…99531585070528807039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.563 Γ— 10⁹⁡(96-digit number)
35637381474327268476…99531585070528807041
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
7.127 Γ— 10⁹⁡(96-digit number)
71274762948654536952…99063170141057614079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.127 Γ— 10⁹⁡(96-digit number)
71274762948654536952…99063170141057614081
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
1.425 Γ— 10⁹⁢(97-digit number)
14254952589730907390…98126340282115228159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.425 Γ— 10⁹⁢(97-digit number)
14254952589730907390…98126340282115228161
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
2.850 Γ— 10⁹⁢(97-digit number)
28509905179461814781…96252680564230456319
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:57,894,061 XPMΒ·at block #6,831,238 Β· updates every 60s
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