XPM Prime Explorer symbol
XPMPrime Explorer

Block #93,674

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/2/2013, 2:25:54 PM Β· Difficulty 9.1961 Β· 6,709,825 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d5917a913831ce7ebf4bcc20bd4d33d0e144d71cf8ae7110ba6090db02dd9330
View on Chainz β†—

Height

#93,674

Difficulty

9.196134

Transactions

2

Size

722 B

Version

2

Bits

093235da

Nonce

204,074

Timestamp

8/2/2013, 2:25:54 PM

Confirmations

6,709,825

Mined by

⛏️ P2SHAK5yHXyyTXWxgn2NRjESu7vyGVCL3mrR9E

Merkle Root

c7554a43035d629b88a887dc5e319d3b4a751614619d96a9edfb0eba7133c6f7
Transactions (2)
Coinbasec5931f99d0130c…03a86f1b3c94d2
1 in β†’ 1 out11.8200 XPM109 B
AK5yHXyy…CL3mrR9E
08983ba5b45a59…99315af09d79cc
3 in β†’ 2 out50.0175 XPM523 B
AFxeKXgU…ig8jLrGNAWBxo1CZ…io9xxbDA
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.

1.338 Γ— 10⁹⁴(95-digit number)
13389881998308830356…93686005533383041899
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
1.338 Γ— 10⁹⁴(95-digit number)
13389881998308830356…93686005533383041899
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.338 Γ— 10⁹⁴(95-digit number)
13389881998308830356…93686005533383041901
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
2.677 Γ— 10⁹⁴(95-digit number)
26779763996617660712…87372011066766083799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.677 Γ— 10⁹⁴(95-digit number)
26779763996617660712…87372011066766083801
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
5.355 Γ— 10⁹⁴(95-digit number)
53559527993235321424…74744022133532167599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.355 Γ— 10⁹⁴(95-digit number)
53559527993235321424…74744022133532167601
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
1.071 Γ— 10⁹⁡(96-digit number)
10711905598647064284…49488044267064335199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.071 Γ— 10⁹⁡(96-digit number)
10711905598647064284…49488044267064335201
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
2.142 Γ— 10⁹⁡(96-digit number)
21423811197294128569…98976088534128670399
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:57,672,023 XPMΒ·at block #6,803,498 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