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Block #2,645,498

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 10:40:32 PM Β· Difficulty 11.7333 Β· 4,193,345 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
30db37574a4fd80689b68a6d1de7c6c87b562e760aadab7a1e7e9433f0a4b002
View on Chainz β†—

Height

#2,645,498

Difficulty

11.733267

Transactions

1

Size

201 B

Version

2

Bits

0bbbb769

Nonce

672,220,443

Timestamp

5/2/2018, 10:40:32 PM

Confirmations

4,193,345

Mined by

⛏️ P2SHAJXpoEByVLv3pCE9xQvRkYe4ycdy2p4K5W

Merkle Root

72a9d029fd59ea5d2712171f0faded310b181c3d53bad58026a31e8536c1f32a
Transactions (1)
Coinbase72a9d029fd59ea…a31e8536c1f32a
1 in β†’ 1 out7.2500 XPM109 B
AJXpoEBy…dy2p4K5W
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.

1.905 Γ— 10⁹⁹(100-digit number)
19056970023560699145…66426618786282864639
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
1.905 Γ— 10⁹⁹(100-digit number)
19056970023560699145…66426618786282864639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.905 Γ— 10⁹⁹(100-digit number)
19056970023560699145…66426618786282864641
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
3.811 Γ— 10⁹⁹(100-digit number)
38113940047121398290…32853237572565729279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.811 Γ— 10⁹⁹(100-digit number)
38113940047121398290…32853237572565729281
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
7.622 Γ— 10⁹⁹(100-digit number)
76227880094242796580…65706475145131458559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.622 Γ— 10⁹⁹(100-digit number)
76227880094242796580…65706475145131458561
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
1.524 Γ— 10¹⁰⁰(101-digit number)
15245576018848559316…31412950290262917119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.524 Γ— 10¹⁰⁰(101-digit number)
15245576018848559316…31412950290262917121
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
3.049 Γ— 10¹⁰⁰(101-digit number)
30491152037697118632…62825900580525834239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.049 Γ— 10¹⁰⁰(101-digit number)
30491152037697118632…62825900580525834241
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
6.098 Γ— 10¹⁰⁰(101-digit number)
60982304075394237264…25651801161051668479
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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