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Block #2,645,767

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 1:34:50 AM Β· Difficulty 11.7383 Β· 4,197,490 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bb0933e8eb5da5273418b6404f2aa54e2b31e1b398c4323cf45b16fa8d5e6b8f
View on Chainz β†—

Height

#2,645,767

Difficulty

11.738299

Transactions

1

Size

200 B

Version

2

Bits

0bbd0123

Nonce

756,811,124

Timestamp

5/3/2018, 1:34:50 AM

Confirmations

4,197,490

Mined by

⛏️ P2SHAezm2rtYpKk12z3CruiT39SBcBB2X5r9tS

Merkle Root

efff7754277897464c61ee9dd53c9e4468b33bdc03a6da7dcf66f6ea688f94ae
Transactions (1)
Coinbaseefff7754277897…66f6ea688f94ae
1 in β†’ 1 out7.2500 XPM110 B
Aezm2rtY…B2X5r9tS
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.

4.917 Γ— 10⁹⁴(95-digit number)
49173933785151896286…49996953602519436159
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
4.917 Γ— 10⁹⁴(95-digit number)
49173933785151896286…49996953602519436159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.917 Γ— 10⁹⁴(95-digit number)
49173933785151896286…49996953602519436161
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
9.834 Γ— 10⁹⁴(95-digit number)
98347867570303792573…99993907205038872319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.834 Γ— 10⁹⁴(95-digit number)
98347867570303792573…99993907205038872321
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
1.966 Γ— 10⁹⁡(96-digit number)
19669573514060758514…99987814410077744639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.966 Γ— 10⁹⁡(96-digit number)
19669573514060758514…99987814410077744641
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
3.933 Γ— 10⁹⁡(96-digit number)
39339147028121517029…99975628820155489279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.933 Γ— 10⁹⁡(96-digit number)
39339147028121517029…99975628820155489281
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
7.867 Γ— 10⁹⁡(96-digit number)
78678294056243034058…99951257640310978559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.867 Γ— 10⁹⁡(96-digit number)
78678294056243034058…99951257640310978561
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
1.573 Γ— 10⁹⁢(97-digit number)
15735658811248606811…99902515280621957119
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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