XPM Prime Explorer symbol
XPMPrime Explorer

Block #259,070

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/13/2013, 10:21:52 AM Β· Difficulty 9.9769 Β· 6,539,971 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c5e0aab17d401b7933a461d48e6b2ca9cd78773b2465ee333d9cfcd48cb7459
View on Chainz β†—

Height

#259,070

Difficulty

9.976934

Transactions

1

Size

199 B

Version

2

Bits

09fa1861

Nonce

6,494

Timestamp

11/13/2013, 10:21:52 AM

Confirmations

6,539,971

Mined by

⛏️ P2SHAZz6Bg87J8VhAYyRKDwNgf7vf5MZtiQn8U

Merkle Root

5872b8b916b089898ca8d101877063a3f82b2e1e7d42bc6a25654bba82b6f463
Transactions (1)
Coinbase5872b8b916b089…654bba82b6f463
1 in β†’ 1 out10.0300 XPM109 B
AZz6Bg87…MZtiQn8U
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.

7.266 Γ— 10⁹³(94-digit number)
72667880723239140268…49066071410237030399
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
7.266 Γ— 10⁹³(94-digit number)
72667880723239140268…49066071410237030399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.266 Γ— 10⁹³(94-digit number)
72667880723239140268…49066071410237030401
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
1.453 Γ— 10⁹⁴(95-digit number)
14533576144647828053…98132142820474060799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.453 Γ— 10⁹⁴(95-digit number)
14533576144647828053…98132142820474060801
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
2.906 Γ— 10⁹⁴(95-digit number)
29067152289295656107…96264285640948121599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.906 Γ— 10⁹⁴(95-digit number)
29067152289295656107…96264285640948121601
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
5.813 Γ— 10⁹⁴(95-digit number)
58134304578591312214…92528571281896243199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.813 Γ— 10⁹⁴(95-digit number)
58134304578591312214…92528571281896243201
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
1.162 Γ— 10⁹⁡(96-digit number)
11626860915718262442…85057142563792486399
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:57,636,368 XPMΒ·at block #6,799,040 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