XPM Prime Explorer symbol
XPMPrime Explorer

Block #157,474

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2013, 3:57:08 PM Β· Difficulty 9.8692 Β· 6,651,426 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cd653a1dc91123439609fc4fea52d87aeaba90f06a6a41dea5cff068df0f9cf9
View on Chainz β†—

Height

#157,474

Difficulty

9.869156

Transactions

1

Size

199 B

Version

2

Bits

09de8102

Nonce

436,387

Timestamp

9/9/2013, 3:57:08 PM

Confirmations

6,651,426

Mined by

⛏️ P2SHAGLpT5zBCy42ej8dmuMEVvxHoCBnHeFXQg

Merkle Root

74d1c97999d4c2341b2b002b21ec6f7adf663aab8c1fd621b124cd15e796307d
Transactions (1)
Coinbase74d1c97999d4c2…24cd15e796307d
1 in β†’ 1 out10.2500 XPM109 B
AGLpT5zB…BnHeFXQg
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.

1.123 Γ— 10⁹⁴(95-digit number)
11232076892205433625…32652482044638985239
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
1.123 Γ— 10⁹⁴(95-digit number)
11232076892205433625…32652482044638985239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.123 Γ— 10⁹⁴(95-digit number)
11232076892205433625…32652482044638985241
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
2.246 Γ— 10⁹⁴(95-digit number)
22464153784410867250…65304964089277970479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.246 Γ— 10⁹⁴(95-digit number)
22464153784410867250…65304964089277970481
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
4.492 Γ— 10⁹⁴(95-digit number)
44928307568821734501…30609928178555940959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.492 Γ— 10⁹⁴(95-digit number)
44928307568821734501…30609928178555940961
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
8.985 Γ— 10⁹⁴(95-digit number)
89856615137643469003…61219856357111881919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.985 Γ— 10⁹⁴(95-digit number)
89856615137643469003…61219856357111881921
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
1.797 Γ— 10⁹⁡(96-digit number)
17971323027528693800…22439712714223763839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,715,253 XPMΒ·at block #6,808,899 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

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy