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Block #546,147

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2014, 5:44:03 PM Β· Difficulty 10.9552 Β· 6,287,264 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f7dfc2d1d91f7c3ff8b309f92551e59b83262160940e84942bb7feae2b336a4f
View on Chainz β†—

Height

#546,147

Difficulty

10.955248

Transactions

2

Size

582 B

Version

2

Bits

0af48b26

Nonce

17,975,666

Timestamp

5/15/2014, 5:44:03 PM

Confirmations

6,287,264

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1a356605f7fa83bf0daf9460f88b98613e2f9aab91f507e4d2065c30a950c47d
Transactions (2)
Coinbaseead9a49bf6f304…86081c3bca197d
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
fc73b9c9cfe1cb…06f553b984afba
2 in β†’ 2 out11.3900 XPM373 B
AHJaoHP6…Z2ha1CR5AMyFarm4…6npGvxsv
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.

1.510 Γ— 10¹⁰²(103-digit number)
15109755246104153591…18438232159169413119
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
1.510 Γ— 10¹⁰²(103-digit number)
15109755246104153591…18438232159169413119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.510 Γ— 10¹⁰²(103-digit number)
15109755246104153591…18438232159169413121
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
3.021 Γ— 10¹⁰²(103-digit number)
30219510492208307183…36876464318338826239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.021 Γ— 10¹⁰²(103-digit number)
30219510492208307183…36876464318338826241
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
6.043 Γ— 10¹⁰²(103-digit number)
60439020984416614367…73752928636677652479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.043 Γ— 10¹⁰²(103-digit number)
60439020984416614367…73752928636677652481
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
1.208 Γ— 10¹⁰³(104-digit number)
12087804196883322873…47505857273355304959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.208 Γ— 10¹⁰³(104-digit number)
12087804196883322873…47505857273355304961
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
2.417 Γ— 10¹⁰³(104-digit number)
24175608393766645746…95011714546710609919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.417 Γ— 10¹⁰³(104-digit number)
24175608393766645746…95011714546710609921
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:57,911,490 XPMΒ·at block #6,833,410 Β· updates every 60s
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