XPM Prime Explorer symbol
XPMPrime Explorer

Block #124,439

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/19/2013, 3:58:05 PM Β· Difficulty 9.7702 Β· 6,671,905 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5e150ba04bafa85725c06a06e247d896c2ffaebe8019fe43b0c949e3f219988d
View on Chainz β†—

Height

#124,439

Difficulty

9.770236

Transactions

2

Size

358 B

Version

2

Bits

09c52e35

Nonce

352,905

Timestamp

8/19/2013, 3:58:05 PM

Confirmations

6,671,905

Mined by

⛏️ P2SHAcXxcJYF95zpQR51vHe5wXcvQvo2UACahh

Merkle Root

05a21a9e77941c5ad3c91e6b1a083d5099ad7b210be1f8eed0d24f7013f28b49
Transactions (2)
Coinbase3a5a353484618b…97a492f605ae29
1 in β†’ 1 out10.4700 XPM109 B
AcXxcJYF…o2UACahh
7282b490de8401…f8a01f6b347f0c
1 in β†’ 1 out10.4900 XPM158 B
AStrCUmY…6B6nwu4h
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.

5.005 Γ— 10⁹⁢(97-digit number)
50052784684796150142…62032668064915937289
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
5.005 Γ— 10⁹⁢(97-digit number)
50052784684796150142…62032668064915937289
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.005 Γ— 10⁹⁢(97-digit number)
50052784684796150142…62032668064915937291
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
1.001 Γ— 10⁹⁷(98-digit number)
10010556936959230028…24065336129831874579
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.001 Γ— 10⁹⁷(98-digit number)
10010556936959230028…24065336129831874581
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
2.002 Γ— 10⁹⁷(98-digit number)
20021113873918460056…48130672259663749159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.002 Γ— 10⁹⁷(98-digit number)
20021113873918460056…48130672259663749161
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
4.004 Γ— 10⁹⁷(98-digit number)
40042227747836920113…96261344519327498319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.004 Γ— 10⁹⁷(98-digit number)
40042227747836920113…96261344519327498321
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
8.008 Γ— 10⁹⁷(98-digit number)
80084455495673840227…92522689038654996639
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:57,614,744 XPMΒ·at block #6,796,343 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