XPM Prime Explorer symbol
XPMPrime Explorer

Block #120,934

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/17/2013, 12:00:39 PM Β· Difficulty 9.7517 Β· 6,710,344 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
923d0b1e5fa4458d774a96dddc40577a8526e5800a2183e8a808ae4a2a1aa67b
View on Chainz β†—

Height

#120,934

Difficulty

9.751692

Transactions

1

Size

201 B

Version

2

Bits

09c06ee8

Nonce

25,773

Timestamp

8/17/2013, 12:00:39 PM

Confirmations

6,710,344

Mined by

⛏️ P2SHAQ9FGFAJqsT3PjKGZwrfCCuZRPCAyw6yEq

Merkle Root

e586fbf5ac61bbef51bce952ea883d24dce41e60d462685d3d774c20959ce8a0
Transactions (1)
Coinbasee586fbf5ac61bb…774c20959ce8a0
1 in β†’ 1 out10.5000 XPM109 B
AQ9FGFAJ…CAyw6yEq
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.

4.936 Γ— 10⁹⁹(100-digit number)
49363791231823772010…54329971360004727309
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
4.936 Γ— 10⁹⁹(100-digit number)
49363791231823772010…54329971360004727309
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.936 Γ— 10⁹⁹(100-digit number)
49363791231823772010…54329971360004727311
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
9.872 Γ— 10⁹⁹(100-digit number)
98727582463647544021…08659942720009454619
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.872 Γ— 10⁹⁹(100-digit number)
98727582463647544021…08659942720009454621
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
1.974 Γ— 10¹⁰⁰(101-digit number)
19745516492729508804…17319885440018909239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.974 Γ— 10¹⁰⁰(101-digit number)
19745516492729508804…17319885440018909241
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
3.949 Γ— 10¹⁰⁰(101-digit number)
39491032985459017608…34639770880037818479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.949 Γ— 10¹⁰⁰(101-digit number)
39491032985459017608…34639770880037818481
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
7.898 Γ— 10¹⁰⁰(101-digit number)
78982065970918035217…69279541760075636959
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:57,894,368 XPMΒ·at block #6,831,277 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.
Privacy PolicyΒ·
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