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Block #1,348,667

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2015, 12:05:36 PM Β· Difficulty 10.8195 Β· 5,476,159 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7e47de386bf2fb515e0a0bbaec215a5ac37a7c99b18fd11875fe9205de20f146
View on Chainz β†—

Height

#1,348,667

Difficulty

10.819461

Transactions

2

Size

6.75 KB

Version

2

Bits

0ad1c833

Nonce

503,295,930

Timestamp

11/30/2015, 12:05:36 PM

Confirmations

5,476,159

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

b4c3ee74cfb83d5066ede62222a3e9f84cfb01b285f3104d056c5e7e30f06928
Transactions (2)
Coinbase80fb7c04d2bd61…c0e6ea9d022c8e
1 in β†’ 1 out8.6000 XPM116 B
AJCEY9yy…tg97E6zm
be05273d4d3625…d520efd11a0843
45 in β†’ 1 out33.7446 XPM6.55 KB
AbecWDS9…1vtToSML
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.

2.731 Γ— 10⁹⁷(98-digit number)
27318607889121575986…65123844354882600959
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
2.731 Γ— 10⁹⁷(98-digit number)
27318607889121575986…65123844354882600959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.731 Γ— 10⁹⁷(98-digit number)
27318607889121575986…65123844354882600961
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
5.463 Γ— 10⁹⁷(98-digit number)
54637215778243151972…30247688709765201919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.463 Γ— 10⁹⁷(98-digit number)
54637215778243151972…30247688709765201921
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
1.092 Γ— 10⁹⁸(99-digit number)
10927443155648630394…60495377419530403839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.092 Γ— 10⁹⁸(99-digit number)
10927443155648630394…60495377419530403841
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
2.185 Γ— 10⁹⁸(99-digit number)
21854886311297260789…20990754839060807679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.185 Γ— 10⁹⁸(99-digit number)
21854886311297260789…20990754839060807681
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
4.370 Γ— 10⁹⁸(99-digit number)
43709772622594521578…41981509678121615359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.370 Γ— 10⁹⁸(99-digit number)
43709772622594521578…41981509678121615361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,842,687 XPMΒ·at block #6,824,825 Β· updates every 60s
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