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Block #160,120

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2013, 4:36:04 PM Β· Difficulty 9.8619 Β· 6,643,353 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4e3044ec52ba1e7a8ac660acb22bee7f3a74596397b4d0c9915c4ef95780a79b
View on Chainz β†—

Height

#160,120

Difficulty

9.861948

Transactions

2

Size

4.43 KB

Version

2

Bits

09dca8a3

Nonce

12,937

Timestamp

9/11/2013, 4:36:04 PM

Confirmations

6,643,353

Mined by

⛏️ P2SHAcMYZ4y2QaHqWJfN2jLS5mi6U3SA8KujQk

Merkle Root

64a9b754b7f54dd0eb43627c859145bf8019bc753e27e7c65b7860ecf04b08f2
Transactions (2)
Coinbase8079878f1f90c2…83307eaed8f1d6
1 in β†’ 1 out10.3200 XPM109 B
AcMYZ4y2…SA8KujQk
11f6b5e18e6eaa…47ce6f49c1ee4a
32 in β†’ 1 out299.9450 XPM4.23 KB
AdQnwzKL…Wao85xMQ
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.

2.320 Γ— 10⁹³(94-digit number)
23206577401966579271…03000053096946278399
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
2.320 Γ— 10⁹³(94-digit number)
23206577401966579271…03000053096946278399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.320 Γ— 10⁹³(94-digit number)
23206577401966579271…03000053096946278401
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
4.641 Γ— 10⁹³(94-digit number)
46413154803933158542…06000106193892556799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.641 Γ— 10⁹³(94-digit number)
46413154803933158542…06000106193892556801
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
9.282 Γ— 10⁹³(94-digit number)
92826309607866317084…12000212387785113599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.282 Γ— 10⁹³(94-digit number)
92826309607866317084…12000212387785113601
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
1.856 Γ— 10⁹⁴(95-digit number)
18565261921573263416…24000424775570227199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.856 Γ— 10⁹⁴(95-digit number)
18565261921573263416…24000424775570227201
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
3.713 Γ— 10⁹⁴(95-digit number)
37130523843146526833…48000849551140454399
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:57,671,812 XPMΒ·at block #6,803,472 Β· updates every 60s
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