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Block #1,073,602

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2015, 12:23:39 PM Β· Difficulty 10.7401 Β· 5,735,804 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f2b267dcb29c1ce26a80be057d313d68b40ff5fc49b9a564fa93b2bbb9b288a7
View on Chainz β†—

Height

#1,073,602

Difficulty

10.740081

Transactions

2

Size

41.13 KB

Version

2

Bits

0abd75f0

Nonce

1,552,890,447

Timestamp

5/24/2015, 12:23:39 PM

Confirmations

5,735,804

Mined by

⛏️ P2SHAWy2Y9YYnaLVmQiK6ABMzeLP3jWsiU78Xe

Merkle Root

e1f813d97ddf32766b2c1f54f19906e06d71e61d16dc3d4f2b1497257d687604
Transactions (2)
Coinbase6ed7341bcacbbc…43f30e0b075219
1 in β†’ 1 out9.1600 XPM109 B
AWy2Y9YY…WsiU78Xe
f38f8f1a185c52…d345c1a71ba572
283 in β†’ 1 out2473.3474 XPM40.94 KB
AamvfYr2…qExEMdKh
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.

2.747 Γ— 10⁹⁡(96-digit number)
27473109187206249016…01733000996843338079
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
2.747 Γ— 10⁹⁡(96-digit number)
27473109187206249016…01733000996843338079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.747 Γ— 10⁹⁡(96-digit number)
27473109187206249016…01733000996843338081
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
5.494 Γ— 10⁹⁡(96-digit number)
54946218374412498032…03466001993686676159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.494 Γ— 10⁹⁡(96-digit number)
54946218374412498032…03466001993686676161
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
1.098 Γ— 10⁹⁢(97-digit number)
10989243674882499606…06932003987373352319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.098 Γ— 10⁹⁢(97-digit number)
10989243674882499606…06932003987373352321
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
2.197 Γ— 10⁹⁢(97-digit number)
21978487349764999212…13864007974746704639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.197 Γ— 10⁹⁢(97-digit number)
21978487349764999212…13864007974746704641
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
4.395 Γ— 10⁹⁢(97-digit number)
43956974699529998425…27728015949493409279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.395 Γ— 10⁹⁢(97-digit number)
43956974699529998425…27728015949493409281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,719,322 XPMΒ·at block #6,809,405 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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