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Block #1,082,004

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2015, 11:12:52 PM Β· Difficulty 10.7672 Β· 5,716,905 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a67838f772a62731bb2c198c1b70ba7ba8f98c70771c5a8750b93d7e541afbe0
View on Chainz β†—

Height

#1,082,004

Difficulty

10.767165

Transactions

1

Size

242 B

Version

2

Bits

0ac464f5

Nonce

390,973,856

Timestamp

5/29/2015, 11:12:52 PM

Confirmations

5,716,905

Mined by

⛏️ P2SHAPGBorYSVyrD2SpRvSHm34b51BQnZrTNSi

Merkle Root

cfaab82c985607af6acdf24825fc228d11ccb5703310b2be4eb8f31f07736270
Transactions (1)
Coinbasecfaab82c985607…b8f31f07736270
1 in β†’ 2 out8.6100 XPM152 B
APGBorYS…QnZrTNSiALPu3s2c…EJXLjVFh
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.

1.695 Γ— 10⁹⁡(96-digit number)
16953368644903481839…15664114429325424639
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
1.695 Γ— 10⁹⁡(96-digit number)
16953368644903481839…15664114429325424639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.695 Γ— 10⁹⁡(96-digit number)
16953368644903481839…15664114429325424641
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
3.390 Γ— 10⁹⁡(96-digit number)
33906737289806963678…31328228858650849279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.390 Γ— 10⁹⁡(96-digit number)
33906737289806963678…31328228858650849281
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
6.781 Γ— 10⁹⁡(96-digit number)
67813474579613927356…62656457717301698559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.781 Γ— 10⁹⁡(96-digit number)
67813474579613927356…62656457717301698561
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
1.356 Γ— 10⁹⁢(97-digit number)
13562694915922785471…25312915434603397119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.356 Γ— 10⁹⁢(97-digit number)
13562694915922785471…25312915434603397121
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
2.712 Γ— 10⁹⁢(97-digit number)
27125389831845570942…50625830869206794239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.712 Γ— 10⁹⁢(97-digit number)
27125389831845570942…50625830869206794241
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:57,635,312 XPMΒ·at block #6,798,908 Β· updates every 60s
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