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Block #2,955,699

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/7/2018, 8:03:46 AM Β· Difficulty 11.3952 Β· 3,885,133 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
699a49c662f40328fceeb799753081b7232fcc01922c3a016609d0b5af5af0fc
View on Chainz β†—

Height

#2,955,699

Difficulty

11.395193

Transactions

1

Size

201 B

Version

2

Bits

0b652b64

Nonce

225,559,508

Timestamp

12/7/2018, 8:03:46 AM

Confirmations

3,885,133

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

89bc98aca161449d100199f262ce4de44837f1a82b2831166a3164c53c2f51a1
Transactions (1)
Coinbase89bc98aca16144…3164c53c2f51a1
1 in β†’ 1 out7.6900 XPM110 B
AUhjokok…k5m93PZR
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.

3.995 Γ— 10⁹⁷(98-digit number)
39956239929874009112…59407167033739182079
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
3.995 Γ— 10⁹⁷(98-digit number)
39956239929874009112…59407167033739182079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.995 Γ— 10⁹⁷(98-digit number)
39956239929874009112…59407167033739182081
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
7.991 Γ— 10⁹⁷(98-digit number)
79912479859748018224…18814334067478364159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.991 Γ— 10⁹⁷(98-digit number)
79912479859748018224…18814334067478364161
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
1.598 Γ— 10⁹⁸(99-digit number)
15982495971949603644…37628668134956728319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.598 Γ— 10⁹⁸(99-digit number)
15982495971949603644…37628668134956728321
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
3.196 Γ— 10⁹⁸(99-digit number)
31964991943899207289…75257336269913456639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.196 Γ— 10⁹⁸(99-digit number)
31964991943899207289…75257336269913456641
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
6.392 Γ— 10⁹⁸(99-digit number)
63929983887798414579…50514672539826913279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.392 Γ— 10⁹⁸(99-digit number)
63929983887798414579…50514672539826913281
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
1.278 Γ— 10⁹⁹(100-digit number)
12785996777559682915…01029345079653826559
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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