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Block #158,912

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2013, 6:04:34 PM Β· Difficulty 9.8658 Β· 6,636,525 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00615850bef3262a14a1bc68fae6bfd5128394e600c9e08c93ed1158677c9505
View on Chainz β†—

Height

#158,912

Difficulty

9.865750

Transactions

2

Size

423 B

Version

2

Bits

09dda1d1

Nonce

57,258

Timestamp

9/10/2013, 6:04:34 PM

Confirmations

6,636,525

Mined by

⛏️ P2SHATpY3yjGz2VkvD9ouyCLzJKmJFxZyYqhas

Merkle Root

a40db5e5bba6fedbaeb23d871e7722bbc3e83024e983369d75b483385d858574
Transactions (2)
Coinbase92c1ab9bce7595…4640d09f026d99
1 in β†’ 1 out10.2700 XPM109 B
ATpY3yjG…xZyYqhas
676288dfda0127…951a043a42ac16
1 in β†’ 2 out0.4900 XPM225 B
APx4VB2a…2ZvafAUSAeL3h4ur…n29hApqS
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.

1.842 Γ— 10⁹³(94-digit number)
18429046015697708302…75375979554520615019
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
1.842 Γ— 10⁹³(94-digit number)
18429046015697708302…75375979554520615019
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.842 Γ— 10⁹³(94-digit number)
18429046015697708302…75375979554520615021
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
3.685 Γ— 10⁹³(94-digit number)
36858092031395416604…50751959109041230039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.685 Γ— 10⁹³(94-digit number)
36858092031395416604…50751959109041230041
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
7.371 Γ— 10⁹³(94-digit number)
73716184062790833208…01503918218082460079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.371 Γ— 10⁹³(94-digit number)
73716184062790833208…01503918218082460081
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
1.474 Γ— 10⁹⁴(95-digit number)
14743236812558166641…03007836436164920159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.474 Γ— 10⁹⁴(95-digit number)
14743236812558166641…03007836436164920161
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
2.948 Γ— 10⁹⁴(95-digit number)
29486473625116333283…06015672872329840319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.948 Γ— 10⁹⁴(95-digit number)
29486473625116333283…06015672872329840321
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:57,607,559 XPMΒ·at block #6,795,436 Β· updates every 60s
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