XPM Prime Explorer symbol
XPMPrime Explorer

Block #312,611

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/15/2013, 2:35:04 AM Β· Difficulty 9.9959 Β· 6,486,972 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b5ac9386dfade58382fa3171046443251b58256be45ff2e0b37f0ed928f04d84
View on Chainz β†—

Height

#312,611

Difficulty

9.995865

Transactions

1

Size

206 B

Version

2

Bits

09fef10a

Nonce

154,959

Timestamp

12/15/2013, 2:35:04 AM

Confirmations

6,486,972

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b83e2f1a6f2563191c36ffe5714989e8f76b3b67ffc95133eaeb87ebc25a790a
Transactions (1)
Coinbaseb83e2f1a6f2563…eb87ebc25a790a
1 in β†’ 1 out9.9900 XPM116 B
AbwWkWZt…kawDhufa
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.

5.400 Γ— 10⁹⁴(95-digit number)
54000800799798587408…66263177460276385119
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
5.400 Γ— 10⁹⁴(95-digit number)
54000800799798587408…66263177460276385119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.400 Γ— 10⁹⁴(95-digit number)
54000800799798587408…66263177460276385121
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
1.080 Γ— 10⁹⁡(96-digit number)
10800160159959717481…32526354920552770239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.080 Γ— 10⁹⁡(96-digit number)
10800160159959717481…32526354920552770241
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
2.160 Γ— 10⁹⁡(96-digit number)
21600320319919434963…65052709841105540479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.160 Γ— 10⁹⁡(96-digit number)
21600320319919434963…65052709841105540481
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
4.320 Γ— 10⁹⁡(96-digit number)
43200640639838869927…30105419682211080959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.320 Γ— 10⁹⁡(96-digit number)
43200640639838869927…30105419682211080961
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
8.640 Γ— 10⁹⁡(96-digit number)
86401281279677739854…60210839364422161919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.640 Γ— 10⁹⁡(96-digit number)
86401281279677739854…60210839364422161921
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:57,640,714 XPMΒ·at block #6,799,582 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK