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Block #2,872,304

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/8/2018, 7:44:36 AM Β· Difficulty 11.6659 Β· 3,971,527 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5bf7fad3108fce0b50ef223457412b0cd8002afbcafc00ada6a355c576f091cf
View on Chainz β†—

Height

#2,872,304

Difficulty

11.665873

Transactions

1

Size

200 B

Version

2

Bits

0baa76af

Nonce

1,261,505,770

Timestamp

10/8/2018, 7:44:36 AM

Confirmations

3,971,527

Mined by

⛏️ P2SHANwVeU574QMQpiuUqhPenagRo7bx66iJfC

Merkle Root

1b19314010ed0b88894cc043a20df42c320f855150af901f71119aea09303b20
Transactions (1)
Coinbase1b19314010ed0b…119aea09303b20
1 in β†’ 1 out7.3400 XPM110 B
ANwVeU57…bx66iJfC
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.

3.960 Γ— 10⁹⁴(95-digit number)
39606114015642266392…82684523340415258999
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
3.960 Γ— 10⁹⁴(95-digit number)
39606114015642266392…82684523340415258999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.960 Γ— 10⁹⁴(95-digit number)
39606114015642266392…82684523340415259001
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
7.921 Γ— 10⁹⁴(95-digit number)
79212228031284532785…65369046680830517999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.921 Γ— 10⁹⁴(95-digit number)
79212228031284532785…65369046680830518001
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
1.584 Γ— 10⁹⁡(96-digit number)
15842445606256906557…30738093361661035999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.584 Γ— 10⁹⁡(96-digit number)
15842445606256906557…30738093361661036001
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
3.168 Γ— 10⁹⁡(96-digit number)
31684891212513813114…61476186723322071999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.168 Γ— 10⁹⁡(96-digit number)
31684891212513813114…61476186723322072001
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
6.336 Γ— 10⁹⁡(96-digit number)
63369782425027626228…22952373446644143999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.336 Γ— 10⁹⁡(96-digit number)
63369782425027626228…22952373446644144001
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
1.267 Γ— 10⁹⁢(97-digit number)
12673956485005525245…45904746893288287999
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
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