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Block #2,635,669

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 7:57:56 AM Β· Difficulty 11.3317 Β· 4,205,640 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e5ff285e1373e37f3081a256837faa8d8f398fae0f72cdf19e89c7b4aea2f6a1
View on Chainz β†—

Height

#2,635,669

Difficulty

11.331674

Transactions

2

Size

870 B

Version

2

Bits

0b54e897

Nonce

85,329,412

Timestamp

4/29/2018, 7:57:56 AM

Confirmations

4,205,640

Mined by

⛏️ P2SHAMVPtKT9fhHNwWPZvMHrNe3ctxv97ybprN

Merkle Root

787bfb8825b478d56e500370d76cb53799d184db878f2d6b36cdba074a5ac084
Transactions (2)
Coinbasee6bb3d172b4058…189afd324bcd8d
1 in β†’ 1 out7.7800 XPM110 B
AMVPtKT9…v97ybprN
c0c45de49976d4…942089f906cc3b
4 in β†’ 2 out5.0717 XPM670 B
AUgHtwXu…kbjJ9aZiAdKhEL4Q…RQS9ZydR
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.

2.715 Γ— 10⁹⁴(95-digit number)
27156954347264839914…40544242793138815279
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
2.715 Γ— 10⁹⁴(95-digit number)
27156954347264839914…40544242793138815279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.715 Γ— 10⁹⁴(95-digit number)
27156954347264839914…40544242793138815281
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
5.431 Γ— 10⁹⁴(95-digit number)
54313908694529679829…81088485586277630559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.431 Γ— 10⁹⁴(95-digit number)
54313908694529679829…81088485586277630561
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
1.086 Γ— 10⁹⁡(96-digit number)
10862781738905935965…62176971172555261119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.086 Γ— 10⁹⁡(96-digit number)
10862781738905935965…62176971172555261121
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
2.172 Γ— 10⁹⁡(96-digit number)
21725563477811871931…24353942345110522239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.172 Γ— 10⁹⁡(96-digit number)
21725563477811871931…24353942345110522241
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
4.345 Γ— 10⁹⁡(96-digit number)
43451126955623743863…48707884690221044479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.345 Γ— 10⁹⁡(96-digit number)
43451126955623743863…48707884690221044481
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
8.690 Γ— 10⁹⁡(96-digit number)
86902253911247487726…97415769380442088959
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:57,974,833 XPMΒ·at block #6,841,308 Β· updates every 60s
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