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Block #1,247,518

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/22/2015, 6:22:30 AM Β· Difficulty 10.7546 Β· 5,592,987 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
94ed8aaf2a0685627c29a8e37ed3a90ee9a502fd8c7cf1ef6b9f5be1ee660ca7
View on Chainz β†—

Height

#1,247,518

Difficulty

10.754569

Transactions

1

Size

199 B

Version

2

Bits

0ac12b6b

Nonce

1,920,734,900

Timestamp

9/22/2015, 6:22:30 AM

Confirmations

5,592,987

Mined by

⛏️ P2SHARtBYtbBFj4q9zx8nordkeZEyw4uYvxD8k

Merkle Root

4ab08c00b1a37f5eb0b7135fffa4b5c25e4333f1476f197818c3f2f7e52630e5
Transactions (1)
Coinbase4ab08c00b1a37f…c3f2f7e52630e5
1 in β†’ 1 out8.6300 XPM109 B
ARtBYtbB…4uYvxD8k
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.

1.535 Γ— 10⁹⁴(95-digit number)
15355243897575805206…84761318735663664039
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
1.535 Γ— 10⁹⁴(95-digit number)
15355243897575805206…84761318735663664039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.535 Γ— 10⁹⁴(95-digit number)
15355243897575805206…84761318735663664041
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
3.071 Γ— 10⁹⁴(95-digit number)
30710487795151610412…69522637471327328079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.071 Γ— 10⁹⁴(95-digit number)
30710487795151610412…69522637471327328081
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
6.142 Γ— 10⁹⁴(95-digit number)
61420975590303220825…39045274942654656159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.142 Γ— 10⁹⁴(95-digit number)
61420975590303220825…39045274942654656161
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
1.228 Γ— 10⁹⁡(96-digit number)
12284195118060644165…78090549885309312319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.228 Γ— 10⁹⁡(96-digit number)
12284195118060644165…78090549885309312321
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
2.456 Γ— 10⁹⁡(96-digit number)
24568390236121288330…56181099770618624639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.456 Γ— 10⁹⁡(96-digit number)
24568390236121288330…56181099770618624641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.913 Γ— 10⁹⁡(96-digit number)
49136780472242576660…12362199541237249279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,968,374 XPMΒ·at block #6,840,504 Β· updates every 60s
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