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Block #676,236

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/13/2014, 12:19:50 PM Β· Difficulty 10.9654 Β· 6,141,003 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a512228f3336be89e7d33da60894030de44762ae4f646399f23cfd78bf2ce367
View on Chainz β†—

Height

#676,236

Difficulty

10.965422

Transactions

2

Size

727 B

Version

2

Bits

0af725e8

Nonce

414,261,890

Timestamp

8/13/2014, 12:19:50 PM

Confirmations

6,141,003

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bf5d3af6977694aed144fd54fcfb43480c7a3a7ba6517ffb22ecf05e15d84402
Transactions (2)
Coinbase33e02b1e3938bb…46fc9c09f295bb
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
a56accb1c579c7…d9b84f56dd40ed
3 in β†’ 2 out997.9103 XPM521 B
AbtTnP8v…KYtpZZDyAcVcaZ5i…t8GBNmpx
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.

2.308 Γ— 10⁹⁡(96-digit number)
23082561054839457862…28852198985806575469
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
2.308 Γ— 10⁹⁡(96-digit number)
23082561054839457862…28852198985806575469
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.308 Γ— 10⁹⁡(96-digit number)
23082561054839457862…28852198985806575471
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
4.616 Γ— 10⁹⁡(96-digit number)
46165122109678915724…57704397971613150939
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.616 Γ— 10⁹⁡(96-digit number)
46165122109678915724…57704397971613150941
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
9.233 Γ— 10⁹⁡(96-digit number)
92330244219357831449…15408795943226301879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.233 Γ— 10⁹⁡(96-digit number)
92330244219357831449…15408795943226301881
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
1.846 Γ— 10⁹⁢(97-digit number)
18466048843871566289…30817591886452603759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.846 Γ— 10⁹⁢(97-digit number)
18466048843871566289…30817591886452603761
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
3.693 Γ— 10⁹⁢(97-digit number)
36932097687743132579…61635183772905207519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.693 Γ— 10⁹⁢(97-digit number)
36932097687743132579…61635183772905207521
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:57,781,944 XPMΒ·at block #6,817,238 Β· updates every 60s
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