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Block #2,964,490

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2018, 4:26:55 PM Β· Difficulty 11.3518 Β· 3,878,722 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f0cff1a017528af5200710ce28bdaf14b9c1f4a4b9e41132ec4b5fa873f8ed63
View on Chainz β†—

Height

#2,964,490

Difficulty

11.351794

Transactions

1

Size

200 B

Version

2

Bits

0b5a0f28

Nonce

396,812,826

Timestamp

12/13/2018, 4:26:55 PM

Confirmations

3,878,722

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

59096988da53f2474054873e88e844f7e957ab0beb7f2609c0e004c47d91a6b6
Transactions (1)
Coinbase59096988da53f2…e004c47d91a6b6
1 in β†’ 1 out7.7500 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.551 Γ— 10⁹⁴(95-digit number)
25516965016025437960…46199184007245745439
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
2.551 Γ— 10⁹⁴(95-digit number)
25516965016025437960…46199184007245745439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.551 Γ— 10⁹⁴(95-digit number)
25516965016025437960…46199184007245745441
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
5.103 Γ— 10⁹⁴(95-digit number)
51033930032050875921…92398368014491490879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.103 Γ— 10⁹⁴(95-digit number)
51033930032050875921…92398368014491490881
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
1.020 Γ— 10⁹⁡(96-digit number)
10206786006410175184…84796736028982981759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.020 Γ— 10⁹⁡(96-digit number)
10206786006410175184…84796736028982981761
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
2.041 Γ— 10⁹⁡(96-digit number)
20413572012820350368…69593472057965963519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.041 Γ— 10⁹⁡(96-digit number)
20413572012820350368…69593472057965963521
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
4.082 Γ— 10⁹⁡(96-digit number)
40827144025640700737…39186944115931927039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.082 Γ— 10⁹⁡(96-digit number)
40827144025640700737…39186944115931927041
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
8.165 Γ— 10⁹⁡(96-digit number)
81654288051281401474…78373888231863854079
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:57,990,069 XPMΒ·at block #6,843,211 Β· updates every 60s
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