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Block #1,534,801

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 11:46:55 AM Β· Difficulty 10.6183 Β· 5,273,759 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ac863fa41e2a3757086753072b0cd20cb8e9e422b86a8e9ce6415fc7afdd22c1
View on Chainz β†—

Height

#1,534,801

Difficulty

10.618323

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e4a68

Nonce

1,292,416,322

Timestamp

4/10/2016, 11:46:55 AM

Confirmations

5,273,759

Mined by

⛏️ P2SHAHABNGjArtJXktBChWWk6yB3tU2AX25JTz

Merkle Root

8cc579b29c00706a1b351aa246bce290f1e07aaf394b9881c7b17651ce8a8bd2
Transactions (2)
Coinbasecf904639b300d3…93253bb55a52df
1 in β†’ 1 out8.9400 XPM109 B
AHABNGjA…2AX25JTz
a4086400f6cd26…9279f7083cc9b8
51 in β†’ 1 out3198.2873 XPM7.41 KB
AKv1NfgT…b1mnv2U8
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.

3.978 Γ— 10⁹⁴(95-digit number)
39786114772382203784…28351894554649117319
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
3.978 Γ— 10⁹⁴(95-digit number)
39786114772382203784…28351894554649117319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.978 Γ— 10⁹⁴(95-digit number)
39786114772382203784…28351894554649117321
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
7.957 Γ— 10⁹⁴(95-digit number)
79572229544764407569…56703789109298234639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.957 Γ— 10⁹⁴(95-digit number)
79572229544764407569…56703789109298234641
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
1.591 Γ— 10⁹⁡(96-digit number)
15914445908952881513…13407578218596469279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.591 Γ— 10⁹⁡(96-digit number)
15914445908952881513…13407578218596469281
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
3.182 Γ— 10⁹⁡(96-digit number)
31828891817905763027…26815156437192938559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.182 Γ— 10⁹⁡(96-digit number)
31828891817905763027…26815156437192938561
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
6.365 Γ— 10⁹⁡(96-digit number)
63657783635811526055…53630312874385877119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.365 Γ— 10⁹⁡(96-digit number)
63657783635811526055…53630312874385877121
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:57,712,538 XPMΒ·at block #6,808,559 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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