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Block #715,127

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2014, 2:05:28 PM Β· Difficulty 10.9545 Β· 6,091,316 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aeaef8d23dc605be58c36f5cc84d432e8d2188394e93de84db250854c20a1d03
View on Chainz β†—

Height

#715,127

Difficulty

10.954502

Transactions

1

Size

207 B

Version

2

Bits

0af45a3a

Nonce

1,415,005,274

Timestamp

9/10/2014, 2:05:28 PM

Confirmations

6,091,316

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

61f82b312a6cc3b2eb1b7e7f39d715998e7f39c3ebe25117d4408be4a4aac8a0
Transactions (1)
Coinbase61f82b312a6cc3…408be4a4aac8a0
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

5.783 Γ— 10⁹⁢(97-digit number)
57839996254253328022…64753363729106046719
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
5.783 Γ— 10⁹⁢(97-digit number)
57839996254253328022…64753363729106046719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.783 Γ— 10⁹⁢(97-digit number)
57839996254253328022…64753363729106046721
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
1.156 Γ— 10⁹⁷(98-digit number)
11567999250850665604…29506727458212093439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.156 Γ— 10⁹⁷(98-digit number)
11567999250850665604…29506727458212093441
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
2.313 Γ— 10⁹⁷(98-digit number)
23135998501701331209…59013454916424186879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.313 Γ— 10⁹⁷(98-digit number)
23135998501701331209…59013454916424186881
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
4.627 Γ— 10⁹⁷(98-digit number)
46271997003402662418…18026909832848373759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.627 Γ— 10⁹⁷(98-digit number)
46271997003402662418…18026909832848373761
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
9.254 Γ— 10⁹⁷(98-digit number)
92543994006805324836…36053819665696747519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.254 Γ— 10⁹⁷(98-digit number)
92543994006805324836…36053819665696747521
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
1.850 Γ— 10⁹⁸(99-digit number)
18508798801361064967…72107639331393495039
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:57,695,633 XPMΒ·at block #6,806,442 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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