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Block #1,208,320

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2015, 6:47:53 PM Β· Difficulty 10.7709 Β· 5,598,461 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d88366665dc8d64f2ba0e607d81d05812e2ddcc8d8ced19523df6d0bd1269608
View on Chainz β†—

Height

#1,208,320

Difficulty

10.770913

Transactions

1

Size

242 B

Version

2

Bits

0ac55a87

Nonce

177,245,385

Timestamp

8/25/2015, 6:47:53 PM

Confirmations

5,598,461

Mined by

⛏️ P2SHAWnU87MoJ1UasjmPcDweSUSWuLuoszwZP3

Merkle Root

de8449d4cd650a36d5186d2bc090c24be6673087a9dba23cb8f922826e8cf95b
Transactions (1)
Coinbasede8449d4cd650a…f922826e8cf95b
1 in β†’ 2 out8.6100 XPM152 B
AWnU87Mo…uoszwZP3ALPu3s2c…EJXLjVFh
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.

2.134 Γ— 10⁹⁡(96-digit number)
21346851468329617715…75493393851627502379
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
2.134 Γ— 10⁹⁡(96-digit number)
21346851468329617715…75493393851627502379
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.134 Γ— 10⁹⁡(96-digit number)
21346851468329617715…75493393851627502381
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
4.269 Γ— 10⁹⁡(96-digit number)
42693702936659235430…50986787703255004759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.269 Γ— 10⁹⁡(96-digit number)
42693702936659235430…50986787703255004761
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
8.538 Γ— 10⁹⁡(96-digit number)
85387405873318470861…01973575406510009519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.538 Γ— 10⁹⁡(96-digit number)
85387405873318470861…01973575406510009521
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
1.707 Γ— 10⁹⁢(97-digit number)
17077481174663694172…03947150813020019039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.707 Γ— 10⁹⁢(97-digit number)
17077481174663694172…03947150813020019041
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
3.415 Γ— 10⁹⁢(97-digit number)
34154962349327388344…07894301626040038079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.415 Γ— 10⁹⁢(97-digit number)
34154962349327388344…07894301626040038081
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:57,698,351 XPMΒ·at block #6,806,780 Β· updates every 60s
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