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Block #149,038

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/4/2013, 2:42:43 AM Β· Difficulty 9.8568 Β· 6,666,046 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e3339907ad34cf7c1e7c5a144a3575ff927a96b01200bf9e59d0f9d178deda64
View on Chainz β†—

Height

#149,038

Difficulty

9.856771

Transactions

1

Size

199 B

Version

2

Bits

09db555a

Nonce

70,592

Timestamp

9/4/2013, 2:42:43 AM

Confirmations

6,666,046

Mined by

⛏️ P2SHAaGBpe6LsP7BAoL6uzic37z3McwpSdaNKU

Merkle Root

41779856a547db40a47f718569ddf3812044728d66595da1819882c49d886145
Transactions (1)
Coinbase41779856a547db…9882c49d886145
1 in β†’ 1 out10.2800 XPM109 B
AaGBpe6L…wpSdaNKU
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.

7.055 Γ— 10⁹⁴(95-digit number)
70559620815383758815…62503345395302808959
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
7.055 Γ— 10⁹⁴(95-digit number)
70559620815383758815…62503345395302808959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.055 Γ— 10⁹⁴(95-digit number)
70559620815383758815…62503345395302808961
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
1.411 Γ— 10⁹⁡(96-digit number)
14111924163076751763…25006690790605617919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.411 Γ— 10⁹⁡(96-digit number)
14111924163076751763…25006690790605617921
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
2.822 Γ— 10⁹⁡(96-digit number)
28223848326153503526…50013381581211235839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.822 Γ— 10⁹⁡(96-digit number)
28223848326153503526…50013381581211235841
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
5.644 Γ— 10⁹⁡(96-digit number)
56447696652307007052…00026763162422471679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.644 Γ— 10⁹⁡(96-digit number)
56447696652307007052…00026763162422471681
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
1.128 Γ— 10⁹⁢(97-digit number)
11289539330461401410…00053526324844943359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,764,759 XPMΒ·at block #6,815,083 Β· updates every 60s
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